Solve for b -1/4(-16b-20)=-7b-16

$- \frac{1}{4} (- 16 b - 20) = - 7 b - 16$

Step 1

Simplify $- \frac{1}{4} \cdot (- 16 b - 20)$ .

Rewrite.

$0 + 0 - \frac{1}{4} \cdot (- 16 b - 20) = - 7 b - 16$

Simplify by adding zeros.

$- \frac{1}{4} \cdot (- 16 b - 20) = - 7 b - 16$

Apply the distributive property.

$- \frac{1}{4} (- 16 b) - \frac{1}{4} \cdot - 20 = - 7 b - 16$

Cancel the common factor of $4$ .

Move the leading negative in $- \frac{1}{4}$ into the numerator.

$\frac{- 1}{4} (- 16 b) - \frac{1}{4} \cdot - 20 = - 7 b - 16$

Factor $4$ out of $- 16 b$ .

$\frac{- 1}{4} (4 (- 4 b)) - \frac{1}{4} \cdot - 20 = - 7 b - 16$

Cancel the common factor.

$\frac{- 1}{4} (4 (- 4 b)) - \frac{1}{4} \cdot - 20 = - 7 b - 16$

Rewrite the expression.

$- 1 (- 4 b) - \frac{1}{4} \cdot - 20 = - 7 b - 16$

Multiply $- 4$ by $- 1$ .

$4 b - \frac{1}{4} \cdot - 20 = - 7 b - 16$

Cancel the common factor of $4$ .

Move the leading negative in $- \frac{1}{4}$ into the numerator.

$4 b + \frac{- 1}{4} \cdot - 20 = - 7 b - 16$

Factor $4$ out of $- 20$ .

$4 b + \frac{- 1}{4} \cdot (4 (- 5)) = - 7 b - 16$

Cancel the common factor.

$4 b + \frac{- 1}{4} \cdot (4 \cdot - 5) = - 7 b - 16$

Rewrite the expression.

$4 b - 1 \cdot - 5 = - 7 b - 16$

Multiply $- 1$ by $- 5$ .

$4 b + 5 = - 7 b - 16$

Step 2

Move all terms containing $b$ to the left side of the equation.

Add $7 b$ to both sides of the equation.

$4 b + 5 + 7 b = - 16$

Add $4 b$ and $7 b$ .

$11 b + 5 = - 16$

Step 3

Move all terms not containing $b$ to the right side of the equation.

Subtract $5$ from both sides of the equation.

$11 b = - 16 - 5$

Subtract $5$ from $- 16$ .

$11 b = - 21$

Step 4

Divide each term in $11 b = - 21$ by $11$ and simplify.

Divide each term in $11 b = - 21$ by $11$ .

$\frac{11 b}{11} = \frac{- 21}{11}$

Simplify the left side.

Cancel the common factor of $11$ .

Cancel the common factor.

$\frac{11 b}{11} = \frac{- 21}{11}$

Divide $b$ by $1$ .

$b = \frac{- 21}{11}$

Simplify the right side.

Move the negative in front of the fraction.

$b = - \frac{21}{11}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$b = - \frac{21}{11}$

Decimal Form:

$b = - 1.\overline{90}$

Mixed Number Form:

$b = - 1 \frac{10}{11}$

Solve for b -1/4(-16b-20)=-7b-16

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